The Senate on Monday moved toward adopting significant changes to the border security provisions in its comprehensive immigration bill, a move seen as crucial to attracting a broad majority of support for the landmark legislation.

Sixty-seven senators, including 15 Republicans, voted to limit debate on a Republican amendment aimed at quelling worries over future border security. The measure would initiate a massive buildup of Border Patrol agents and the completion of 700 miles of fencing along the U.S.-Mexico border before legalized immigrants can obtain permanent residence.

The vote on the proposal, which was co-written by Sens. Bob Corker (R-Tenn.) and John Hoeven (R-N.D.), clears the way for a final vote on the overall bill later this week. The amendment is likely the last major change to underlying bill that will be considered ahead of the vote before the full Senate, which is expected Thursday.

Supporters of the bill fell just shy of the 70-vote total they had hoped for in part due to travel delays. Six senator did not vote, several having not made it to Washington on time. The bill's backers are looking for 70 votes in favor of the overall legislation in order to cajole the GOP-controlled House of Representatives to act on comprehensive immigration reform.

But with 15 Republicans backing the motion and zero Democratic defections, supporters were happy with the with the total.

"I think we're building momentum and I'm really gratified that we had [that] number of votes," Corker told reporters after the vote. "There's no question it was crucial [to picking up GOP support]. I was involved in discussions and knew the vote count."

Corker, one of the authors of the bill, had chided other Republican senators who said that his amendment does not go far enough to secure the southern border. He cited the fact that well-known border hawk Jan Brewer -- Arizona's GOP governor -- called the proposal a "victory" for her state.

"Do you want to vote against this, really?" a fiery Corker asked his colleagues during a speech on the Senate floor earlier on Monday.

In addition to doubling the Border Patrol and constructing more fencing, the amendment would make it mandatory for businesses to verify the immigration status of potential employees and implement exit tracking of visas at all air and sea ports.

The nonpartisan Congressional Budget Office projected that the amendment would reduce the flow of undocumented immigrants into the U.S., relative to the existing bill. But the budget office also estimated that the bill would reduce the deficit by about $40 billion less than originally projected.

But some GOP critics said it simply added more resources to border enforcement efforts instead of focusing on tangible results. And others dubbed it a "fig leaf" for Republicans to use as cover to vote for the broader bill. Twenty-six Republicans voted against the bill.

"Fundamentally, it's about political coverage and not solving the problem," Sen. Ted Cruz (R-Texas) remarked on the floor.

Democratic supporters of the bill have explained they accepted the language as means to attract more GOP support because it does not block the path to citizenship for undocumented immigrants.

"We all want border security, but we didn't want border security [to] be used as a pretext to block the path to citizenship, and that was what the fight was," Sen. Chuck Schumer (D-N.Y.) said on Univision's "Al Punto" last Sunday. "We overcame that a couple of days ago where we said we were not having any of these 'triggers' that are not attainable on border security, which would prevent the earned path to citizenship."

But the House is a different story. Most members of the Republican-controlled body appear to be unconvinced by the compromise border language. And some House Republicans are moving ahead with an effort to handle immigration reform on a piece-by-piece basis.

"It will pass the Senate, but it's dead on arrival in the House," Sen. Rand Paul (R-Ky.) said on CNN's "State of the Union" last Sunday. "The House is much closer to me, and I think they think border security has to come first before you get immigration reform."